Final answer:
An equilateral triangle has all sides equal in length. To find the length of one side, we can use the Pythagorean theorem. By plugging in the values and solving the equation, the length of one side of the equilateral triangle is approximately 6.93 cm.
Step-by-step explanation:
An equilateral triangle has all sides equal in length. The altitude of an equilateral triangle is a line segment drawn from one vertex to the opposite side, creating a right angle with the base. Since the triangle is equilateral, the altitude bisects the base and creates two congruent right-angled triangles.
Using the Pythagorean theorem, we can find the length of one side of the equilateral triangle. The altitude acts as the height of the right-angled triangle, and half of the base acts as the base of the right-angled triangle.
Using the Pythagorean theorem, we can write:
a^2 = b^2 + c^2
Where 'a' is the hypotenuse (which is the side of the equilateral triangle), 'b' is half of the base, and 'c' is the altitude.
Plugging in the values, we have:
a^2 = (0.5s)^2 + 6^2
a^2 = 0.25s^2 + 36
Since the triangle is equilateral, all sides are equal, so 'a' represents one side of the triangle. Therefore, a = s. We can substitute this into the equation:
s^2 = 0.25s^2 + 36
Simplifying the equation, we have:
0.75s^2 = 36
Dividing both sides by 0.75, we get:
s^2 = 48
Finally, taking the square root of both sides, we find:
s = sqrt(48)
Therefore, the length of one side of the equilateral triangle is approximately 6.93 cm.